scholarly journals A Proximal Fully Parallel Splitting Method for Stable Principal Component Pursuit

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Hongchun Sun ◽  
Jing Liu ◽  
Min Sun
Keyword(s):  
Signal Processing ◽  
Statistical Learning ◽  
Splitting Method ◽  
Principal Component ◽  
Computational Results ◽  
Closed Form Solutions ◽  
Mild Conditions ◽  
Separable Convex Programming ◽  
Parallel Splitting ◽  
Principal Component Pursuit

As a special three-block separable convex programming, the stable principal component pursuit (SPCP) arises in many different disciplines, such as statistical learning, signal processing, and web data ranking. In this paper, we propose a proximal fully parallel splitting method (PFPSM) for solving SPCP, in which the resulting subproblems all admit closed-form solutions and can be solved in distributed manners. Compared with other similar algorithms in the literature, PFPSM attaches a Glowinski relaxation factor η∈3/2,2/3 to the updating formula for its Lagrange multiplier, which can be used to accelerate the convergence of the generated sequence. Under mild conditions, the global convergence of PFPSM is proved. Preliminary computational results show that the proposed algorithm works very well in practice.

Modified proximal symmetric ADMMs for multi-block separable convex optimization with linear constraints

2021 ◽  
pp. 1-28
Author(s):  
Yuan Shen ◽  
Yannian Zuo ◽  
Liming Sun ◽  
Xiayang Zhang
Keyword(s):  
Convex Optimization ◽  
Splitting Method ◽  
Principal Component ◽  
Convergence Result ◽  
Linear Constraints ◽  
Convex Optimization Problem ◽  
Separable Convex Programming ◽  
Separable Convex Optimization ◽  
Linearly Constrained ◽  
Correction Step

We consider the linearly constrained separable convex optimization problem whose objective function is separable with respect to [Formula: see text] blocks of variables. A bunch of methods have been proposed and extensively studied in the past decade. Specifically, a modified strictly contractive Peaceman–Rachford splitting method (SC-PRCM) [S. H. Jiang and M. Li, A modified strictly contractive Peaceman–Rachford splitting method for multi-block separable convex programming, J. Ind. Manag. Optim. 14(1) (2018) 397-412] has been well studied in the literature for the special case of [Formula: see text]. Based on the modified SC-PRCM, we present modified proximal symmetric ADMMs (MPSADMMs) to solve the multi-block problem. In MPSADMMs, all subproblems but the first one are attached with a simple proximal term, and the multipliers are updated twice. At the end of each iteration, the output is corrected via a simple correction step. Without stringent assumptions, we establish the global convergence result and the [Formula: see text] convergence rate in the ergodic sense for the new algorithms. Preliminary numerical results show that our proposed algorithms are effective for solving the linearly constrained quadratic programming and the robust principal component analysis problems.

Atmospheric radar signal processing using principal component analysis

2014 ◽  
Vol 32 ◽  
pp. 79-84 ◽  
Author(s):  
D. Uma Maheswara Rao ◽  
T. Sreenivasulu Reddy ◽  
G. Ramachandra Reddy
Keyword(s):  
Principal Component Analysis ◽  
Signal Processing ◽  
Principal Component ◽  
Component Analysis ◽  
Radar Signal ◽  
Radar Signal Processing

scholarly journals Stable Analysis of Compressive Principal Component Pursuit

Algorithms ◽  
2017 ◽  
Vol 10 (1) ◽  
pp. 29
Author(s):  
Qingshan You ◽  
Qun Wan
Keyword(s):  
Principal Component ◽  
Principal Component Pursuit

scholarly journals Non-Adaptive Methods for Fetal ECG Signal Processing: A Review and Appraisal

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3648 ◽  
Author(s):  
Rene Jaros ◽  
Radek Martinek ◽  
Radana Kahankova
Keyword(s):  
Signal Processing ◽  
Wavelet Transforms ◽  
Principal Component ◽  
Fetal Monitoring ◽  
Adaptive Methods ◽  
Component Analysis ◽  
Adaptive Signal Processing ◽  
Extensive Literature ◽  
Fetal Electrocardiogram ◽  
Fetal Ecg

Fetal electrocardiography is among the most promising methods of modern electronic fetal monitoring. However, before they can be fully deployed in the clinical practice as a gold standard, the challenges associated with the signal quality must be solved. During the last two decades, a great amount of articles dealing with improving the quality of the fetal electrocardiogram signal acquired from the abdominal recordings have been introduced. This article aims to present an extensive literature survey of different non-adaptive signal processing methods applied for fetal electrocardiogram extraction and enhancement. It is limiting that a different non-adaptive method works well for each type of signal, but independent component analysis, principal component analysis and wavelet transforms are the most commonly published methods of signal processing and have good accuracy and speed of algorithms.

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